The renormalization of \(\Pi _{{\perp \perp }}(z)\)  and \(\Pi _{{\parallel \perp }}(z)\)  is determined by their
respective ADs, \(\gamma _{\parallel \perp }\)  and \(\gamma _{\perp \perp }\) , which are currently known to two-loop accuracy
[1]}, [2]}, [3]}. Notice that the renormalization factors are
local, i.e., they do not depend on the distance between the fields. They can be interpreted as
the renormalization factors of local “heavy-light” operators in an effective field theory
(see Refs. [1]}, [2]}, [3]} for details).
